Question

7.) The set of prime numbers less than 20 is (2, 3, 5, 7, 11, 13, 17, 19}.a) How many subsets can be formed that contain exactly 3 elements?b) How many subsets can be formed that contain at least 1 element?

Answer 1

7) a

Total number of elements in the set = 8

We want to select k subsets that contain exactly 3 elements each. We can get k by applying the combination formula. It is written as

nCr = n!/r!(n - r)!

In this case, n = 8 and r = 3

number of 3 element subsets = 8!/3!(8 - 3)!

number of 3 element subsets = 56

7b) For a containing n elements, the number of subsets that can be formed is 2^n. This also includes an empty set. Since we are considering subsets with at least one element, The number of subsets would be 2^n - 1

Given that n = 8,

number of subsets = 2^8 - 1 = 256 - 1

number of subsets = 255